Wales international Ashley Williams and Everton could both be sanctioned by UEFA after a brawl instigated by the Welshman saw a fan holding a child appear to aim a punch at a Lyon player.
Toffees skipper Williams' shove on Lyon's goalkeeper after the hour mark sparked heated confrontations between several Everton and Lyon players in front of the Howard Kendall Gwladys Street End.
A supporter holding a child in one arm also appeared to push Lopes in the head and seemed to aim a punch in the direction of the keeper.
Merseyside Police announced they are to investigate the crowd trouble at Goodison Park.
An incensed Williams seemed to raise his hand to Lucas Tousart's face but only received a yellow card, along with Lyon striker Bertrand Traore for the incident.
Williams later went on to score, cancelling out Nabil Fekir's penalty but Traore's 75th-minute-winner earned Lyon a 2-1 success.
Everton boss Ronald Koeman said Williams needs to "control himself".
"By frustration you get maybe more aggression, and that's not bad - but you need to control yourself," the Dutchman said at his press conference on Friday afternoon.